आईफोन 15 का लॉन्च हो चुका है और इसकी शुरुआती कीमत 79,900 रुपये है, जिसके कारण यह एक महंगा स्मार्टफोन माना जा रहा है। इसके बावजूद, लोग इसे अपना बनाने के लिए तैयार हैं, और इसके प्रति उत्सुक हैं। अब, जब आईफोन 15 जैसे पैसेवल्यू गैजेट का आगमन होता है, तो धोखाधड़ी करने वालों के …
Installing USB drivers can vary depending on your operating system and the specific device you want to connect to your computer. Here are general steps for installing USB drivers on Windows Windows:
Real Numbers 1. Euclid’s Algorithm for HCF: Euclid, a Greek mathematician, devised an interesting method to find the HCF of two numbers. This method is known as Euclid’s Algorithm. An algorithm is a stepwise process to solve a problem. Steps taken to find the HCF of two numbers are as under: 1. Identify the greater …
Exercise 3.3 1.Solve the following pair of linear equations by the substitution method : Sol. (i) The given system of equations is x +3 = 14 …(1) and, x-y = 4 …(2) Substituting y = 14-x in (2), we get x – (14 -x) = 14 => x-14 x = 4=> 2x = 4 + …
Exercise 3.2 1.Form the pair of linear equations in the following problems, and find •their solution graphically. Hence, the cost of one pencil is Rs 3 and that of one pen is Rs 5.Verification: Put x = 3 and y = 5 in (1) and (2), we find that both the equations are satisfied. 2.On …
EXERCISE 3.1 1.Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be”. (Isn’t this interesting) ? Represent this situation algebraically and graphically. Sol.Let us denote the present age of daughter and her …
PAIR OF LINEAR EQUATIONSIN TWO VARIABLES 1.Two linear equations in the same two variables are called a pair of linear equations in two variables, or briefly, a linear pair. The most general form of a linear pair is a1x,+b1y +c1=0 a2x +b2y + C2 = 0 where a1, a2, b1, b2, C1, C2 are real …
EXERCISE 2.4 1.Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: (i) 2×2+ x2 – 5x + 2; , 1,-2 (ii) x3 – 4×2 + 5x – 2; 2, 1, 1 Sol. (i) Comparing the given polynomial …
EXERCISE 2.3 1.Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) p(x) = x3-3×2+ 5x – 3, g (x) = x2 _ 2(ii) p(x) =x3 + 3×2+ 4x, g(x) = x2 + 1-x(iii) p(x) = x4– 5x+ 6, g(x) = 2 – x2 Sol. …
EXERCISE 2.2 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients: (i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6×2 – 3 – 7x (iv)4u2 +8u (v) t2 – 15 (vi) 3×2 – x – 4 Sol. (i) We have, x2 – 2x – 8 = x2 – 2x …